In all mechanical drive, gear transmission has characteristics of steady drive, accuracy of drive ratio, high efficiency, long service life or the like, so that the gear transmission becomes the most important and widely used mechanism transmission High speed steady and precise gear transmission is a national key scientific and technological project. A transmission error has been widely accepted and considered as an excitation source for vibration and noise of a gear system because the transmission error affects force and velocity changes in the gear transmission. At the same time, the gear dynamic transmission error is also a very important part in gear testing, so that accurate testing and calculation of the transmission error are of great significance to gear manufacturing and the researches on gear dynamics.
The State Intellectual Property Office of the People's Republic of China disclosed a patent documentation on 1 Oct. 2008, with a Publication Patent No. of CN101275881, and titled Small Mode Number Gear transmission Error Measuring Method, including the steps of firstly connecting a measured gear, a driver, a first goniometric coder, a first shaft joint and a first electric motor in successive, then connecting a measuring gear, a flexible shaft joint, a second goniometric coder, a second shaft joint and a second electric motor in successive, the measured gear and the measuring being meshed in a single side and being driven by the two electric motors respectively, detecting an angular displacement ϕ2 of the measuring gear relative to the second goniometric coder, an angular displacement ϕ1 of a measuring gear shaft system and an angular displacement ϕ′ of a measured gear shaft system, and obtaining a transmission error of a small mode number gear after calculation. However, due to gear machining errors, installation errors, lubrication, modification and other factors, an offset of a tooth profile surface relative to an ideal tooth profile position will lead to a gear backlash (FIG. 1), so that positions of a meshing-in point and a meshing-out point will deviate from a theoretical meshing point when the gear is meshed in or meshed out, to produce corner meshing and cause a collision impact between meshing gear surfaces. Such collision impact plays a key role in smoothness and accuracy of high-speed gear transmission. For accuracy drive, trace idle stroke and impact occur during positive and reverse rotating, which affect the drive accuracy. Obviously, the gear backlash directly affects a gear system to obtain the transmission error. However, the influence of the gear backlash on the transmission error is not considered in this solution, so that a larger deviation will occur between a final calculation result and an actual value.
At the same time, the numerical calculation of the transmission error of the gear system becomes an increasingly prominent problem. At present, transmission error calculation methods stay in the traditional methods, such as: a Newmark integral method, a Runge-Kutta integral method, a Gear method and an improved Gear method (Wstiff method and Dstiff method). The above calculation methods have different emphasis on the transmission error calculation methods. Some methods focus more on grasping the calculation accuracy; while some methods have a faster calculation velocity. The traditional calculation methods usually fail to control the distribution of calculation time and calculation accuracy perfectly, often bring an enormous calculation quantity in case that the accuracy requirement is higher, resulting in a long calculation time; and will decrease the calculation accuracy in case of guaranteeing the calculation time, so that the transmission error of the gear system cannot be described and forecasted correctly.